Question

Suppose we have a whale population that has been declines to 1000 individuals. The growth rate is 2% a year and the carrying capacity is 10,000. Calculate (use Excel) how many years are needed to have the population recover to 5,000 or more, meaning that during those years, no harvesting can take place. Once the population is recovered, how many whales can be harvested per year in a sustainable way?

Answer 1

Given the whale population = 1000

Growth rate = 2%

Carrying capacity = 1000

Years needed to have population of 5000

if the first year, the whale population is x

then the second year, the population is 1.2*x

third year, 1.2*1.2*x

hence, (1.2)^n * 1000 = 5000

1.2^n = 5

applying logarthim on both sides

n * ln (1.2) = ln(5)

n = 8.82 years

now till 8.82 we dont harvest any whales

at 9th year, the whale population is 5159.

at 10 th year, the whale population is 6192

we have (10000-6192) = 3807 whales can be additionally harvested till its capacity.